+ Probability January 07, 2013

+ Riddle Me This.. What always runs but never walks, often murmurs, never talks, has a bed but never sleeps, has a mouth but never eats? A river

+ Kick Off Order the numbers from least to greatest. 1. 7, 4, 15, 9, 5, , 21, 36, 54, 22 Divide. 2, 4, 5, 7, 9, 15 21, 22, 36, 54, ,275  ,125    4

+ Learn to find the mean, median, mode, and range of a data set. Objective

+ mean median mode range outlier Vocabulary

+ The mean is the sum of the data values divided by the number of data items. The median is the middle value of an odd number of data items arranged in order. For an even number of data items, the median is the average of the two middle values. The mode is the value or values that occur most often. When all the data values occur the same number of times, there is no mode. The range of a set of data is the difference between the greatest and least values. It is used to show the spread of the data in a data set. Mean, Median, Mode, & Range The mean is sometimes called the average. Helpful Hint

+ Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 Additional Example 1: Finding the Mean, Median, Mode, and Range of Data mean: Add the values = Divide the sum by the number of items items The mean is sum 8  = Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 Additional Example 1 Continued median: Arrange the values in order. 1, 2, 2, 2, 4, 4, 7, 8 There are two middle values, so find the mean of these two values. The median is = 6 6  2 = 3 Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 Additional Example 1 Continued mode: The value 2 occurs three times. 1, 2, 2, 2, 4, 4, 7, 8 The mode is 2. Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 Additional Example 1 Continued range: Subtract the least value 1, 2, 2, 2, 4, 4, 7, 8 The range is 7. from the greatest value. – 1 =87 Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 Check It Out: Example 1 mean: Add the values = Divide the sum items The mean is sum by the number of items. 8  = Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 Check It Out: Example 1 Continued median: Arrange the values in order. 1, 2, 3, 4, 5, 5, 6, 8 There are two middle values, so find the mean of these two values. The median is = 9 9  2 = 4.5 Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 Check It Out: Example 1 Continued mode: The value 5 occurs two times. 1, 2, 3, 4, 5, 5, 6, 8 The mode is 5. Mean, Median, Mode, & Range

+ Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 Check It Out: Example 1 Continued range: Subtract the least value 1, 2, 3, 4, 5, 5, 6, 8 The range is 7. from the greatest value. – 1 =87 Mean, Median, Mode, & Range

+ MeasureMost Useful When mean median mode The data are spread fairly evenly The data set has an outlier The data involve a subject in which many data points of one value are important, such as election results. Mean, Median, Mode, & Range

+ In the data set below, the value 12 is much less than the other values in the set. An extreme value such as this is called an outlier xx x x x x x x Mean, Median, Mode, & Range 35, 38, 27, 12, 30, 41, 31, 35

+ The data shows Sara’s scores for the last 5 math tests: 88, 90, 55, 94, and 89. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with the outlier. Additional Example 3: Exploring the Effects of Outliers on Measures of Central Tendency outlier55 55, 88, 89, 90, 94 Mean, Median, Mode, & Range

+ Additional Example 3 Continued outlier 55 55, 88, 89, 90, 94 With the Outlier =  5 = 83.2 The mean is , 88, 89, 90, 94 The median is 89.There is no mode. mean:median:mode: Mean, Median, Mode, & Range

+ Additional Example 3 Continued 55, 88, 89, 90, 94 Without the Outlier =  4 = The mean is , 89, 90, 94 The median is 89.5.There is no mode. mean:median:mode: + 2 = 89.5 Mean, Median, Mode, & Range

+ Since all the data values occur the same number of times, the set has no mode. Caution! Mean, Median, Mode, & Range

+ Adding the outlier decreased the mean by 7.05 and the median by 0.5. The mode did not change. Additional Example 3 Continued The median best describes the data with the outlier. Mean, Median, Mode, & Range

+ Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. The tell which measure of central tendency best describes the data with the outlier. 63, 58, 57, 61, 42 Check It Out: Example 3 outlier42 42, 57, 58, 61, 63 Mean, Median, Mode, & Range

+ Check It Out: Example 3 Continued outlier 42 42, 57, 58, 61, 63 With the Outlier =  5 = 56.2 The mean is , 57, 58, 61, 63 The median is 58.There is no mode. mean:median:mode: Mean, Median, Mode, & Range

+ Check It Out: Example 3 Continued 42, 57, 58, 61, 63 Without the Outlier =  4 = The mean is , 58, 61, 63 The median is 59.5.There is no mode. mean:median:mode: + 2 = 59.5 Mean, Median, Mode, & Range

+ Adding the outlier decreased the mean by 3.55 and decreased the median by 1.5. The mode did not change. Check It Out: Example 3 Continued The median best describes the data with the outlier. Mean, Median, Mode, & Range

+ Choose a partner. One partner will get a SPS from the bin and a set of dice. Together you will complete the “Mean, Median, Mode Practice Activity” on the SPS. When you are finished, raise your hand so that I can check your work. If you are correct, you may erase the SPS, return your materials to the bin, and begin your homework. If not, fix your mistakes and raise your hand to be checked again. HW: WB 7-2, page 59